Description
Solution
如果向有一条下界为、上界为的边,那么从向、向连一条流量为的边,从向连一条的边。当最大流等于时,有可行流。
Code
跑得好慢哇,LOJ上都排到倒数第二版了。
/************************************************
* Au: Hany01
* Date: Jul 19th, 2018
* Prob: 无源汇上下界可行流
* Inst: Yali High School
************************************************/
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef pair<int, int> PII;
#define File(a) freopen(a".in", "r", stdin), freopen(a".out", "w", stdout)
#define rep(i, j) for (register int i = 0, i##_end_ = (j); i < i##_end_; ++ i)
#define For(i, j, k) for (register int i = (j), i##_end_ = (k); i <= i##_end_; ++ i)
#define Fordown(i, j, k) for (register int i = (j), i##_end_ = (k); i >= i##_end_; -- i)
#define Set(a, b) memset(a, b, sizeof(a))
#define Cpy(a, b) memcpy(a, b, sizeof(a))
#define x first
#define y second
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) ((int)(a).size())
#define INF (0x3f3f3f3f)
#define INF1 (2139062143)
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define y1 wozenmezhemecaia
template <typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
template <typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; }
inline int read() {
static int _, __; static char c_;
for (_ = 0, __ = 1, c_ = getchar(); c_ < '0' || c_ > '9'; c_ = getchar()) if (c_ == '-') __ = -1;
for ( ; c_ >= '0' && c_ <= '9'; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
return _ * __;
}
const int maxn = 205, maxm = 10205 * 6;
int n, m, S, T, v[maxm], nex[maxm], beg[maxn], e = 1, d[maxn], gap[maxn], f[maxm], Ans, tot;
struct Edge { int u, v, f1, f2; }E[10205];
inline void add(int uu, int vv, int ff, int mk = 1) {
v[++ e] = vv, f[e] = ff, nex[e] = beg[uu], beg[uu] = e;
if (mk) add(vv, uu, 0, 0);
}
int sap(int u, int flow)
{
if (u == T) return flow;
register int res = flow, tmp;
for (register int i = beg[u]; i; i = nex[i]) {
if (d[u] != d[v[i]] + 1 || !f[i]) continue;
tmp = sap(v[i], min(res, f[i]));
f[i] -= tmp; f[i ^ 1] += tmp;
if (!(res -= tmp)) return flow;
}
if (!--gap[d[u]]) d[S] = T;
++ gap[++ d[u]];
return flow - res;
}
int main()
{
#ifdef hany01
File("loj115");
#endif
n = read(), m = read(), T = (S = n + 1) + 1;
For(i, 1, m)
E[i].u = read(), E[i].v = read(), tot += E[i].f1 = read(), E[i].f2 = read(),
add(S, E[i].v, E[i].f1), add(E[i].u, E[i].v, E[i].f2 - E[i].f1), add(E[i].u, T, E[i].f1);
for (gap[0] = T; d[S] < T; ) Ans += sap(S, INF);
if (Ans < tot) { puts("NO"); return 0; }
puts("YES");
For(i, 1, m) printf("%d\n", f[(i - 1) * 6 + 5] + E[i].f1);
return 0;
}